I don't recall seeing or hearing any estimate as a percentage. Back in the 90's I applied on the advice of a psychiatrist, a therapist, and my MD. When my case was denied they told me that most or almost everyone is initially denied. I went back to playing music where it's sort of okay to be crazy.
I applied again about two years ago. My doctor and the doctor hired by SS for the evaluation both said I wasn't able to work. SS admin disagreed. I had an attorney but he forgot to file the appeal on time. An SS employee contacted me and said I should file a special appeal due to the attorney's error. I did. It was denied. I'll either sink or swim. Kind of dogpaddling ATM. I really would like to have all the money back that I paid into the program